Today's deal poses the sort of problem to which there is no good answer. South should make a response with five high-card points, taking a chance of getting too high, both in the hope of finding a spade fit and to avoid making it easy for the enemy to compete. On the next round, he should use his discretion to end the auction by passing two no-trump, since unless playing the Wolff signoff it may not be possible to stop in three spades. More on that later.

When West leads the club six against two no-trump, South wins dummy’s club 10 and leads the spade five. East should now think before automatically playing low. He should work out that it may be advantageous (and cannot cost anything) if he can be the defender to lead the second round of clubs. He should therefore split his spade honors to prevent declarer from ducking the trick to West. Equally, if declarer wins the spade ace, West must also avoid the automatic play of following with his small spade. He must unblock his queen, so that declarer cannot duck the next lead in spades to him, thereby preventing his partner from leading through declarer’s vulnerable club king. After each defender sacrifices a spade honor at his first turn, the contract is doomed.

The Wolff signoff, by the way, is a call of three clubs over the two no-trump rebid, after which a three-spade call by responder at his next turn is an attempt to play there.

After South suggests a slam by cue-bidding five diamonds, North should suggest a choice of slams, no-trump being a plausible option from his perspective because of his club holding. But South should prefer to bid the slam in his solid trump suit with the lead coming up to his diamond ace-queen, rather than risking playing in no-trump with no honor in North's diamond suit.

Against the heart slam, West might lead the club six to deny an honor, but let us say that West leads the club three, the partnership playing fourth-highest leads. When declarer plays the queen from dummy, East must plan his defense carefully.

West’s lead marks South with at least three clubs, and the bidding indicates that South has strong spades and the diamond ace. East must therefore resist the temptation to take his club ace, thus preventing declarer from obtaining a sure later entry to dummy’s heart suit.

Instead, East should follow to trick one with his small club. After East ducks the opening club lead, South can establish the heart suit but cannot return to dummy to use it for discards. He will lead up to dummy’s club holding, but will not be able to guess the suit successfully, so the slam will fail.

Of course, if South tries to run the heart suit by means of finessing against the queen, East can win the heart queen and cash the club ace to set the contract.

?

Against four spades West leads the heart two, his conventional agreement being partner leads low from any three-card holding. How should you plan the play?

At the table declarer put up the jack, and East won his king and shifted to the diamond jack. South tried for an endplay by playing three rounds of diamonds after drawing trumps, but West won and played the heart eight through. Whether declarer covered or not, the defenders had safe exits in the heart suit. In the end South could do no better than take the club finesse for his contract. It lost.

Declarer can do better — but he must play low from dummy at trick one. East wins the heart nine and shifts to the diamond jack. Declarer takes the ace and king, East unblocking the 10 and indicating an original two- or three-card diamond suit in the process.

Next, declarer cashes the spade king and queen, then exits with the diamond eight. West wins and has no palatable choice. A trump to dummy’s ace sees declarer win and then endplay East with the heart queen by discarding a club from hand. Declarer makes the same play if West shifts directly to hearts. A diamond by West gives a ruff-sluff, while a club is no better. If he plays a low club, dummy also plays low and East is endplayed. If he shifts to the club jack, dummy’s queen is played and East wins his king, but must then concede the 10th trick.

Facing anything but a third-in-hand opening, North would have enough to drive to game over South's opening bid. But as a passed hand, he can, if he wants, describe his values precisely with a fit-jump, showing spades and a source of tricks in hearts.

After West leads a top diamond against four spades, South must duck the opening lead, playing the diamond nine from his hand (so West will not later have the opportunity of underleading his diamond queen). He must then attempt to establish dummy’s heart suit for discards without allowing East to gain the lead for the fatal shift to a club.

When West leads a second diamond, South should win, draw two rounds of trump, and lead a heart toward dummy. Now if West plays the heart king, declarer must duck. If West plays a low heart, declarer may play either the queen or ace (the ace may be a slightly better play, guarding against East’s having a singleton king). However, assuming South finesses the queen successfully, he must next return to his hand with a trump and lead another heart toward dummy and duck when West plays the king. If West discards the heart king on the third trump, declarer must cash dummy’s remaining high heart and lead a club to the jack. West will have two clubs to cash, but then must concede a ruff-sluff.

Just for the record, if West leads the heart king at trick two, South must also duck this trick.

When South heard his partner show a strong hand he had a way to make a mild slam try in spades, and North was happy to accept.

Declarer won the opening diamond lead and drew two rounds of trump, then crossed to a top heart and ruffed a diamond, stripped off the hearts and exited with a third spade, hoping to receive a club shift. However, West had a safe exit with his fourth heart, and declarer had to concede a club trick in the end.

Instead of exiting with a trump at trick eight, declarer should ruff another diamond in hand. Now West must pitch a club — if he overruffs he is endplayed, either to lead a club, or to give declarer a ruff and discard.

At this point declarer finesses in clubs and ruffs the last diamond, and now West is caught in an unusual squeeze. While West has no real need to retain his last heart, if he discards it, declarer exits with the last spade. West is endplayed and must lead clubs round to declarer, and the defense’s sure trick has vanished.

West’s only chance here is to bare his club king instead of throwing the 13th heart — now South may misread the position, by leading his last trump and trying to endplay West with his trump trick. Then West would have the 13th heart to cash.

Of course declarer may not misguess the position, but you have to give him the chance to go wrong!

With such excellent fits in hearts and clubs, East-West had little difficulty in reaching their heart slam when South relayed for shape and found first extra shape, then a spade control. The auction was accurate and efficient, the play less so.

When West led the spade 10, declarer won in dummy and crossed to a trump to ruff a spade, crossed to a top club to ruff a second spade, then took a second top trump and found the bad news.

With no tricks available to him, he could do little but exit with two more rounds of trumps, hoping West had started with only three spades. But that player could win and cash out the spades to set the slam.

When in with the spade ace, declarer can count 13 tricks without a finesse if trumps split 3-2, but he should take precautions against a 4-1 break — after all, that happens frequently enough to make it worthwhile to give up on the chances of an overtrick.

By leading a trump from dummy and ducking East’s nine, South then has sufficient entries and trumps to win 12 tricks without the risk of playing on diamonds. After a diamond return, South wins and ruffs a spade in dummy, comes to the club king to ruff a second spade, then draws trump, pitching diamonds from the board. He can now run the clubs and score his three top trumps, two aces, five clubs and two spade ruffs for his 12 tricks.

When the three bears returned from the duplicate club, Goldilocks did not have to ask how things had gone, since Mama Bear immediately thrust the hand records in front of her and asked for sympathy.

In today’s deal she had sat West and had led a spade against two hearts. The defenders took their ruff, but Mama had led back a high spade to the third trick to ask for a diamond. Her partner obliged, but the defenders could now take only one diamond and one heart trick, so the contract came home. Had Mama signaled for a club, the defenders could have avoided any endplay — so long as Mama subsequently hopped up with the heart ace and exited in that suit.

At another table Papa Bear had declared two hearts on a club lead. He won in hand and led a heart; West took her ace, then gave her partner the spade ruff, and East thoughtfully exited with a second club. Now declarer had to lose two diamonds whatever he did.

Goldilocks noted that Baby Bear was waiting impatiently to be asked what he had done on the deal. “I was declaring two hearts on a club lead and cashed both clubs, ending in hand. Then I led a heart up, and West won and played for the spade ruff. The difference was that when East ruffed the third spade, he had no choice but to give me a ruff-sluff with a club, or open up diamonds to my advantage.”

It is almost three decades since the death of one of the world's stars, Oswald Jacoby. Ossie played in the first Culbertson challenge match in 1929, but continued to win national titles into the 1980s, when dying from cancer.

Not only was Jacoby the youngest-ever actuary, but his skill with numbers led to his being referred to as a human computer. He lied about his age in order to serve in World War I, and re-enlisted to serve in counterintelligence in both World War II and the Korean War.

The following hand demonstrates his skill, and illustrates the danger of a defender painting too clear a picture of his hand.

North’s two-diamond bid showed hearts, allowing Jacoby as South to volunteer a bid at the three-level over East’s revealing two-suiter bid. The defense against four hearts started well enough with two top spades and a ruff, and East switched to a diamond. Jacoby won the ace and made the essential play of a heart to the seven, East pitching a club. This was followed by the heart ace, East discarding a second club.

When Jacoby led a trump to his king, East could see that if he discarded a diamond, declarer would be able to ruff out his diamond honor, so he let a third club go. Declarer ruffed a club in dummy, came to his diamond king, ruffed a second club, dropping the ace, and his hand was now high.